\section{The Fundamental Theorem of Field Theory}

\begin{definition}[Extension Field]
	A field $\E$ is an \textit{extension field} of a field $\F$ if $\F \subseteq \E$ and the operations of $\F$ are those of $\E$ restricted to $\F$.
\end{definition}

\begin{theorem}[Fundamental Theorem of Field Theory (Kronecker's Theorem, 1887)]
	Let $\F$ be a field and let $f(x)$ be a nonconstant polynomial in $\F[x]$. Then there is an extension field $\E$ of $\F$ in which $f(x)$ has a zero.
\end{theorem}